In the figure, ABCD is a quadrilateral where ∠ABC = 133° and ∠BCD = 116°. ∠CDE = 79° and BC = CD. The point E on AD is such that BE is parallel to CD. Calculate
- ∠BDE
- ∠BAE
(a)
∠CDB
= (180° - 116°) ÷ 2
= 32° (Isosceles triangle)
∠BDE
= 79° - 32°
= 47°
(b)
∠BAE
= 360° - 116° - 79° - 133°
= 32° (Sum of angles in a quadrilateral)
Answer(s): (a) 47°; (b) 32°